{"paper":{"title":"On some classes of Lindel\\\"of Sigma-spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Oleg Okunev, Paul J. Szeptycki, Wieslaw Kubis","submitted_at":"2005-11-24T11:03:58Z","abstract_excerpt":"We consider special subclasses of the class of Lindel\\\"of Sigma-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space $X$ is in the class $L\\Sigma(\\leq\\kappa)$ if it admits a cover by compact subspaces of weight $\\kappa$ and a countable network for the cover. We restrict our attention to $\\kappa\\leq\\omega$. In the case $\\kappa=\\omega$, the class includes the class of metrizably fibered spaces considered by Tkachuk, and the $P$-approximable spaces considered by Tkacenko. The case $\\kappa=1$ corresponds to the spaces of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511606","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}